He isn't dabbling in British politics -- he's dabbling in his own. For various reasons, the US generally regards the UK's continued membership of the EU as in its interests. Why should he not say so?
The wider point here is that Brexit is not really at all just an issue for the UK. It will have an impact on our relationship with pretty much the entire world. With the European Union, obviously; with the rest of the world less obviously perhaps, but then as we're part of the EU we are often seen in that context on certain issues, so that in many cases people negotiating with the UK were doing so either through the EU or with that in mind. Leaving will change those relationships in complex ways -- if nothing else by creating one extra country to deal with as a separate entity, which creates what might be seen as unnecessary hassle.
Feel free to ignore it, but telling the rest of the world that they shouldn't even speak is pretty disrespectful. And this, bear in the mind, is the world you are intending to be more open to if Brexit happens. Telling that world to sod off is a poor start to the intended brighter future that await us once we let go the shackles of the corrupt dictatorship that is the EU (or whatever the latest overblown rhetoric is).
Of course, it's ultimately a decision for the British people, and it's not at all unreasonable for them to put local interests first. It's just a shame that so many people seem to think that the UK's interests and those of the rest of the world are so different.